Finite Group DatabasebetaFinite Group Databasebeta| order | 1232 |
| isoclinism | isoclinic class of D7×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D77⋊C8 |
| derived, Hall | C7×C11 ⋊ C2×C8 |
| Sylow | C11 ⋊ C8×D7 |
| Sylow | C7 ⋊ C8×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D7×D11 |
| commutator, hypocenter | C7×C11 | C2×C8 |
| Fitting, cosocle | C4×C7×C11 | C22 |
| socle | C2×C7×C11 | C2×C4 |
| prime radical | C2×D77 | C4 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 616 |
Polycyclic presentation:
2^4,7,11|a^2=c,b^2=c,c^2=d,f^a=f^10,e^b=e^6140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1232, 7);